1. Field
The present disclosure relates to thermoelectric devices and related fabrication methods. More in particular, it relates to methods and devices for controlling thermal conductivity and thermoelectric power of semiconductor nanowires. It also relates to electric power generators and refrigerators based on semiconductor nanowires. More specifically, the semiconductor nanowires generate electric power wherever a temperature difference exists. They can also be used in reverse as refrigerators whenever an electric current travels through the nanowires.
2. Related Art
Semiconductors are a class of materials whose electronic properties can be tailored from metallic to insulating. This is accomplished through a process called “doping” whereby a small amount of impurity atoms are injected into the semiconductor by ion implantation or diffusion. Semiconductors can either be made to conduct electrons or holes. Silicon is an example of a semiconductor. For example, silicon is made electron conducting by injection of phosphorus dopants whereas boron dopants make silicon hole conducting. Dopants that render semiconductors electron-rich are called n-type dopants and dopants that render semiconductors hole-rich are called p-type dopants. In general, the electrical conductivity is proportional to the concentration of injected dopants. Thus, the electronic properties can be precisely controlled by controlling the amount of injected dopants. The widespread use of semiconductors in the microelectronic industry is mainly due to the incredible control over their electronic properties.
Nanowires are a class of materials that have length scales for their diameter or width on the order of nanometers to tens of nanometers. The nanometer scale is not easily accessible using conventional lithographic patterning methods found in the microelectronic industry. Instead, the nanoscale may be made accessible using nanowire patterning or nanowire materials growth methods. Typically, nanowires have an aspect ratio (length divided by width or diameter) that is equal to 10n where n typically varies from 1 to 5. The following literature provides representative examples of the fabrication of semiconductor nanowires and their doping:                1. Melosh, N. A. et al. Ultra-high density nanowire lattices and circuits. Science 300, 112-115 (2003).        2. Wang, D., Sheriff, B. A. & Heath, J. R. Complementary symmetry silicon nanowire logic: Power-efficient inverters with gain. Small 2, 1153-1158 (2006).        3. Morales, A. M. & Lieber, C. M. A laser ablation method for the synthesis of semiconductor crystalline nanowires. Science 279, 208-211 (1998).These three documents are incorporated herein by reference in their entirety.        
Thermoelectrics or thermoelectric materials are a class of materials that convert temperature differences into electricity and vice versa. Such materials utilize the Seebeck effect for power generation and the Peltier effect for refrigeration. In the Seebeck effect, a temperature gradient across a thermoelectric material causes the diffusion of charged carriers across that gradient, thus creating a voltage difference between the hot and cold ends of the material. Conversely, the Peltier effect explains the fact that when current flows through a material a temperature gradient arises because the charged carriers exchange thermal energy at the contacts. Therefore, thermoelectric materials can act as either electric power generators in the presence of a temperature difference or as refrigerators when electric current is supplied.
Thermoelectrics are effectively engines that perform these functions without moving parts and they do not pollute. This makes them highly reliable and more importantly attractive as clean power systems, especially at a time when global warming is a growing concern. Other approaches toward power generation or cooling such as fossil fuel based engines emit pollution but are more efficient. As a result, thermoelectrics find only limited use because of their poor efficiency.
The efficiency of a thermoelectric material is determined by the dimensionless figure of merit,
      ZT    =                                        S            2                    ⁢          σ                κ            ⁢      T        ,where S is the thermoelectric power, defined as the thermoelectric voltage, V, produced per degree temperature difference
      S    =                  ⅆ        V                    ⅆ        T              ,σ is the electrical conductivity, κ is the thermal conductivity, and T is the temperature. To maximize ZT, and thus the efficiency, S should be large so that a small temperature difference can create a large voltage, a should be large in order to minimize joule heating losses, and κ should be small to reduce heat leakage and maintain the temperature difference. There is no intrinsic limit to how large ZT can be, but it is generally appreciated that a material with a ZT>1 constitutes a thermoelectric of sufficient efficiency to have at least some practical applications. A thermoelectric with a ZT>3 would be transformative—for example, thermoelectric-based cooling would replace existing compression cycle refrigerators, and thermopower applications for heat recovery or energy conversion would find widespread applications. Currently, the best commercially available thermoelectric devices at room temperature are alloys of Bi2Te3 and have a ZT of ˜1 which corresponds to a Carnot efficiency of ˜10%. Bi2Te3 is an exotic and expensive material to manufacture and thus finding a thermoelectric material with a ZT>1 that is earth abundant and cheap to process would allow more widespread use of thermoelectric devices. Finding a material with a ZT>1, however, is challenging because optimizing one physical parameter often adversely affects another. The following literature provides reviews of thermoelectric devices:                4. MacDonald, D. K. C. Thermoelectricity: An Introduction to the Principles (Wiley, N.Y., 1962).        5. Mahan, G., Sales, B. & Sharp, J. Thermoelectric materials: New approaches to an old problem. Phys. Today 50, 42-47 (1997).        6. Chen, G. et al. Recent developments in thermoelectric materials. Int. Mater. Rev. 48, 45-66 (2003).        7. Majumdar, A. Enhanced: Thermoelectricity in semiconductor nanostructures. Science 303, 777-778 (2004).These four documents are incorporated herein by reference in their entirety.        
In order to demonstrate an efficient thermoelectric, it is important to measure the three material parameters S, σ, and κ, and so calculate ZT. Such measurements can be carried out on nanowires using a variety of on-chip thermometry and electrical leads. The nanowire electrical conductivity is measured by using a 4-point measurement to eliminate contact resistance. For measurement of S and κ, a temperature difference is created across the ends of the nanowires by sourcing a DC current through one of the resistive heaters. The resistance rise of each thermometer is recorded simultaneously using a lock-in measurement as the temperature is ramped upwards. The resistance of the thermometers is typically two orders of magnitude smaller than the nanowire array. For measurement of S, the thermoelectric voltage, as a response to the temperature difference, is recorded using a nano-voltmeter. A difference measurement is used to determine K. The following literature provides representative examples of measurements on thermoelectric devices:                8. Boukai, A., Xu., K. & Heath, J. R. Size-dependent transport and thermoelectric properties of individual polycrystalline bismuth nanowires. Advanced Materials 18, 864-869 (2006).        9. Yu-Ming, L. et al. Semimetal-semiconductor transition in Bi1-xSbx alloy nanowires and their thermoelectric properties. Applied Physics Letters 81, 2403-2405 (2002).        10. Small, J. P., Perez, K. M. & Kim, P. Modulation of thermoelectric power of individual carbon nanotubes. Physical Review Letters 91, 256801 (2003).        11. Li, S et al. Measuring thermal and thermoelectric properties of one-dimensional nanostructures using a microfabricated device. Journal of Heat Transfer 125, 881-888 (2003).        12. Li, D. et al. Thermal conductivity of individual silicon nanowires. Applied Physics Letters 83, 2934-2936 (2003)These five documents are incorporated herein by reference in their entirety.        
In the following paragraphs, the challenges in optimizing the three thermoelectric materials parameters are delineated. In addition, the requirements for a practical thermoelectric device are described. Included in each description are the current state-of-the-art procedures and systems for the best thermoelectric devices.
The thermoelectric power varies between different materials. In general, it has been found that the thermoelectric power is approximately 100 times larger for semiconductors than metals. This is the main reason that semiconductors are the material of choice for thermoelectric devices. The magnitude of the thermoelectric power for a semiconductor depends on the doping concentration. Typically, the thermoelectric power is larger for low doped semiconductors and smaller for highly doped semiconductors. In addition, the thermoelectric power usually decreases as the temperature is lowered for highly doped semiconductor metallic systems. However, some semiconductors, such as silicon, have the unique property that their thermoelectric power increases when the temperature is lowered. This behavior is due to phonon drag.
One physical phenomena that, in very specific systems, can increase S, is phonon drag. Phonon drag results when the phonons collide with either electrons or holes and thus impart their momentum to the electronic carriers. The phonons are in essence “pushing” the electrons and holes down the temperature gradient. This results in an extra amount of electronic carriers diffusing down the temperature gradient and a larger voltage develops than would otherwise normally occur if phonon drag was absent. Phonon drag, therefore, leads to a larger thermoelectric power. Phonon drag has long been known to occur in low-doped semiconductors whose electrical conductivity is poor. Therefore, phonon drag has not been successfully exploited in a practical thermoelectric devices since the low electrical conductivity reduces ZT. Increases in the thermoelectric power would be very beneficial as long as no degradation of the electrical conductivity occurs since the thermoelectric power is squared in the expression for ZT. The following literature provides representative examples of observations of phonon drag on semiconductor thermoelectric devices:                13. Weber, L. & Gmelin, E. Transport properties of silicon. Applied Physics A: Solids and Surfaces 53, 136-140 (1991).        14. Herring, C. Theory of the thermoelectric power of semiconductors. Physical Review 96, 1163-1187 (1954).        15. Geballe, T. H. & Hull, G. W. Seebeck Effect in Silicon. Physical Review 98, 940-947 (1955).        16. Behnen, E. Quantitative examination of the thermoelectric power of n-type silicon in the phonon drag regime. Journal of Applied Physics 67, 287-292 (1990).        17. Trzcinksi, R., Gmelin, E. & Queisser, H. J. Quenched Phonon Drag in Silicon Microcontacts. Phys. Rev. Lett. 56, 1086-1089 (1986).These five documents are incorporated herein by reference in their entirety.        
The electrical conductivity of a semiconductor can be controlled through the doping concentration of impurity atoms. A large doping concentration will result in a large electrical conductivity. In contrast, a low doping concentration will result in a low electrical conductivity. Also, a high doping concentration will result in a lower thermoelectric power so that there is an optimal doping concentration that maximizes S2 σ, otherwise known as the power factor. Most semiconducting thermoelectric devices are doped to a concentration of 1019 cm3. This is no easy task for commercially available thermoelectric devices, a majority of which consist of exotic materials. The doping concentration of silicon (and other relatively simple semiconductors such as germanium), on the other hand, can easily be controlled with high precision. Silicon, therefore, is a promising candidate for highly efficient thermoelectrics since its power factor can be optimized. Unfortunately, bulk silicon is characterized by a large thermal conductivity, and this limits the ZT of silicon to near 0.01. The small ZT precludes the use of bulk silicon thermoelectric devices from entering the commercial market.
The thermal conductivity varies widely for many thermoelectric materials. In general, good thermoelectrics have a thermal conductivity below 10 W m−1 K−1. Silicon, for example, has a thermal conductivity ˜150 W m−1 K−1 at room temperature making it impractical for commercial use. Commercial thermoelectrics based on Bi2Te3 materials have a thermal conductivity of 3 W m−1 K−1 or lower at room temperature. This value, in combination with its favorable power factor leads to a ZT of ˜1 at room temperature. Recently, several groups have used nanostructured materials to increase ZT by using two-dimensional superlattices (i.e. layers of thin films) and zero-dimensional “quantum dots” which have a reduced thermal conductivity relative to their bulk counterparts. However, the materials used in these studies are expensive and rare, and it is not always possible to achieve high efficiencies for both p- and n-type conductors. It is not always straightforward to even prepare both p- and n-type conductors of these systems. Thermopower and thermocooling applications require both p- and n-type thermoelectric materials. The following literature provides representative examples of observations of high ZT on semiconductor thermoelectric devices due to decreased thermal conductivity:                18. Venkatasubramanian, R. et al. Thin-film thermoelectric devices with high room-temperature figures of merit. Nature 413, 597-602 (2001).        19. Harman, T. C. et al. Quantum dot superlattice thermoelectric materials and devices. Science 297, 2229-2232 (2002).        20. Hsu, K. F. et al. Cubic AgPbmSbTe2+m: Bulk thermoelectric materials with high figure of merit. Science 303, 818-821 (2004).These three documents are incorporated herein by reference in their entirety.        
Any practical thermoelectric device contains both p- and n-type doped semiconductor elements alternately connected electrically in series and thermally in parallel (as shown in FIG. 1A). One pair of p- and n-type doped semiconductor elements connected in this manner is called a thermocouple. To increase the output voltage, many thermocouples are connected together. The voltage output is given by NVTE where N is the number of thermocouples and VTE is the thermoelectric voltage of one thermocouple. The following reference, incorporated herein by reference in its entirety, describes methods to fabricate p- and n-type thermoelectric elements that are connected electrically in series and thermally in parallel:                21. Snyder, G. J. et al. Thermoelectric microdevice fabricated by a MEMS-like electrochemical process. Nature Materials 2, 528-531 (2003)        
It is often difficult to dope a semiconductor both p- and n-type. It can also be difficult to precisely control the doping concentration. Silicon, germanium, and their alloys, however, have a distinct advantage over other semiconductors because they can easily be doped p- and n-type. Moreover, repeated and controlled doping of silicon nanowires has been demonstrated. The following reference, incorporated herein by reference in its entirety, describes methods to dope silicon semiconductor nanowires both p- and n-type:                22. Wang, D., Sheriff, B. A. & Heath, J. R. Complementary symmetry silicon nanowire logic: Power-efficient inverters with gain. Small 2, 1153-1158 (2006).        
In summary, the majority of bulk semiconductors are typically poor thermoelectrics either due to their large thermal conductivity and/or small electrical conductivity. Also, current thermoelectric devices do not take advantage of phonon drag effects. In a typical thermoelectric, the three material parameters thermal conductivity, electrical conductivity, and thermopower are interdependent.